For anyone else - Ensure you use the online check-in as soon as this opens, it'll reduce your chances of being downgraded.
Remember that when travelling with an infant, BA seating policy anyone travelling with an infant can choose their seat at the time of booking and change at any time until they have checked in.
You should be able to use the online checkin if you have stated that you're travelling with an infant, or contact your local BA Exectuive office.
Happy travelling.
francismc